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This paper proposes structure-preserving neural surrogates for partial differential equations that integrate Gaussian process regression to provide tractable uncertainty quantification, enabling real-time simulation with closed-form error estimates.
This paper proposes an uncertainty-aware multi-fidelity framework based on conditional normalizing flows to improve the predictive accuracy of reduced-order models (ROMs) for complex multiscale systems. The method learns a probabilistic mapping from low-fidelity to high-fidelity coefficients and is demonstrated on a vortex merging problem, showing improved accuracy with uncertainty quantification.